The present invention relates generally to the field of optics, and more specifically, to a distributed aperture optical systems having means for correcting field-dependent phase errors. In particular, the invention relates to the use of a corrector plate is placed at or near the intermediate focus of a collector telescope to control distortion in a prescribed manner to eliminate the phasing error over the field of view.
As modern telescope systems become larger and larger in aperture, it no longer becomes practical, based on cost and weight considerations, to build single aperture, monolithic, telescopes. One relatively recent improvement in the telescope art has allowed the construction of large aperture systems using a plurality of smaller telescopes that are optically linked together. Such optical systems are called distributed aperture telescopes. One such telescope is shown in U.S. Pat. No. 5,905,591 to Duncan et al.
As seen in the Duncan et al. patent, a distributed or xe2x80x9cmulti-aperturexe2x80x9d imaging system includes a plurality of subaperture telescopes, each of which collects image data of an instantaneous field of view of an extended object scene within a field of regard of the imaging system. The image data collected by each is transferred by respective optical paths to a beam combiner which combines all the image data coherently to form a single high-resolution image of the object scene at a focal plane of the beam combiner.
In general, the optical system of the type described in the Duncan et al. patent includes three modules: (1) a group of afocal telescopes (called the xe2x80x9ccollectorxe2x80x9d telescopes), (2) a plurality of flat mirrors that direct the light from the collectors (called the xe2x80x9crelayxe2x80x9d group) to (3) a common combining telescope (called the xe2x80x9ccombinerxe2x80x9d telescope). The collector telescopes, the relay group and the combiner telescope thus constitute a distributed aperture system.
In distributed aperture optical systems, it is desirable that the collector telescopes have as large a phased field of view possible. In other words, all portions of the image generated by the various apertures are registered and in phase with each other. A major limitation on this phased field of view is known as the xe2x80x9csine magnification error.xe2x80x9d This error is caused by collector telescope magnification variations over the field of view. If the magnification of the collectors follow the sine ratio,                     sin        ⁡                  (                      a            o                    )                            sin        ⁡                  (                      a            i                    )                      =    m    ,
where ai is the input angle and ao is the output angle of the collector telescope, and m is constant, the sine magnification error and thus the phase error over the field would be zero. The field dependent phase error at a particular point in the field, with a baseline L, is given by             p      k        =          L      ⁢              xe2x80x83            ⁢              sin        ⁡                  (                      a            ik                    )                    ⁢                        (                                    m              k                        -                          m              o                                )                          m          o                      ,
where mo represents a xe2x80x9cparaxialxe2x80x9d value for the sine ratio m and mk is the sine ratio computed for field point k. In the context of the present invention, the fractional sine magnification error at field point k is defined as             s      k        =                  (                              m            k                    -                      m            o                          )                    m        o              ,
The sine magnification error in a telescope is essentially a distortion term. Distortion in these telescopes is largely determined by the telescope form, i.e., a two mirror, three mirror, or four or five mirror design. The simplest collector telescope design that has a flat image plane, i.e., a zero Petzval sum, and a real exit pupil is a three-mirror anastigmat (xe2x80x9cTMAxe2x80x9d). These characteristics are essential to the successful operation of a distributed aperture telescope system, as noted in the aforementioned Duncan et al. patent. Unfortunately, a TMA has sine magnification errors. These errors can be mitigated to some extent by using a small instantaneous field of view and adjusting the position of the apertures in the exit pupil (known as xe2x80x9cre-mapping the exit pupilxe2x80x9d), when the field is steered over a larger field of regard (xe2x80x9cFORxe2x80x9d).
This internal steering of the field is described in the Duncan et al. patent. In this way, only a part of the sine magnification phase error is relevant, and re-mapping the exit pupil allows the majority of the phase error to be removed. IF the sine magnification error is sufficiently small, the instantaneous field of view is limited only by vignetting of the light by the optical elements. Furthermore, with small sine magnification errors, minimal pupil re-mapping as a function of FOR would be required. Only one steering mirror would be required to accomplish FOR steering when that mirror is located at the exit pupil of the collector telescope.
Thus, is would be beneficial to keep the TMA collector design as simple as possible, while at the same time correcting its sine magnification error.
The present invention involves the use of an optical element placed near the intermediate image of a TMA or other optical system. This element corrects phase error, but has little or no optical power, and little or no effect on image quality. In a surprising manner, the optical device corrects the sine magnification error without the use of complicated lens or other optical systems, and does so without a negative impact on the quality of the image.
The optical element can be reflective or refractive. In a refractive embodiment, the optical element has a flat surface and an opposite, corrective surface which is defined by a rotationally symmetric polynomial. The polynomial is of the general form   z  =                    cy        2                    1        +                              1            -                                          (                                  k                  +                  1                                )                            ⁢                              c                2                            ⁢                              y                2                                                          +          Dy      4        +          Ey      6        +          Fy      8        +          Gy      10      
where z is the departure from a plane, and y is the radial coordinate on the surface. D, E, F, G, C and K are parameters which are varied during the design process to minimize the sine magnification error. These parameters represent aspheric coefficients, while c is a vertex curvature and k is a conic constant.
One aspect of the present invention is the process of designing and positioning the phase error corrector. First, a plurality of chief rays are traced from different field points. For each of these rays, the fractional sine magnification error sk=(mkxe2x88x92mo)/mo is computed. The surface shape parameters of the phase error corrector and its position are then varied to globally minimize the square of these fractional sine errors. For the example described herein, the corrector surface is rotationally symmetric, and has the form of the aforementioned polynomial. The D, E, F, G, c, and k parameters are varied during the design process to minimize the sine magnification error. If the maximum allowable phase error for a distributed aperture system with baseline L is p, then the fractional sine magnification errors of the collector must satisfy the equation       s    k    ≤      p          L      ⁢              xe2x80x83            ⁢              sin        ⁡                  (                      a            ik                    )                    
for every point in the field of view.
The many advantages of the invention will become more apparent from the following detailed description when taken in conjunction with the illustrative embodiments in the accompanying drawings.